ESSEX COUNTY COLLEGE
Mathematics and Physics Division
MTH 103 – Fundamental Concepts of Modern Mathematics I
Course Outline
Course Number & Name: MTH 103 Fundamental Concepts of Modern Mathematics I
Credit Hours: 4 .0
Contact Hours: 4.0
Lecture: 4.0
Lab: N/A
Other: N/A
Prerequisites: Grade of “C” or better in MTH 092 or placement
Co-requisites: None
Concurrent Courses: None
Course Outline Revision Date: Fall 2010
Course Description: This survey course covers fundamental concepts in Mathematics. An emphasis is
placed on illustrating the impact of mathematics as a historical cultural force. Topics are chosen from
logic, set theory, mathematical systems, number theory, algebra, geometry, and probability and
statistics. Diverse applications are emphasized throughout the course.
General Education Goals: MTH 103 is affirmed in the following General Education Foundation Category:
Quantitative Knowledge and Skills. The corresponding General Education Goal is as follows: Students
will use appropriate mathematical and statistical concepts and operations to interpret data and to solve
problems.
Course Goals: Upon successful completion of this course, students should be able to do the following:
1. demonstrate knowledge of the fundamental concepts and theories from logic, set theory,
mathematical systems, number theory, algebra, geometry, and probability and statistics;
2. utilize various problem-solving and critical-thinking techniques to set up and solve application
problems taken from a variety of disciplines;
3. communicate accurate mathematical terminology and notation in written and/or oral form in order
to explain strategies to solve problems as well as to interpret found solutions; and
4. use calculators effectively as a tool to solve such problems as those described above.
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Measurable Course Performance Objectives (MPOs): Upon successful completion of this course,
students should specifically be able to do the following:
1. Demonstrate knowledge of the fundamental concepts and theories from logic, set theory,
mathematical systems, number theory, algebra, geometry, and probability and statistics:
1.1 use inductive and deductive reasoning to solve mathematical problems;
1.2 perform basic operations on sets including the union, intersection, difference, and Cartesian
product of sets;
1.3 implement primitive procedures such as the Egyptian algorithm, Russian peasant method, lattice
method, and nines complement method;
1.4 convert between number bases;
1.5 find the greatest common factor and least common multiple of a set of numbers;
1.6 graph lines in the Rectangular Coordinate System;
1.7 find areas and volumes of geometric figures; and
1.8 apply counting methods
2. Utilize various problem-solving and critical-thinking techniques to set up and solve application
problems taken from a variety of disciplines:
2.1 solve varied real-world applications using problem-solving strategies such as making a table or a
chart, looking for a pattern, applying inductive reasoning, and using trial and error
3. Communicate accurate mathematical terminology and notation in written and/or oral form in order
to explain strategies to solve problems as well as to interpret found solutions:
3.1 write and explain solutions to application problems related to the course material using
appropriate mathematical terminology and notation
4. Use calculators effectively as a tool to solve such problems as those described above:
4.1 use a calculator to perform basic arithmetic operations such as evaluating powers and roots
Methods of Instruction: Instruction will consist of a combination of lectures, class discussions, group
work, board work, computer lab work, and individual study.
Outcomes Assessment: Test and exam questions are blueprinted to course objectives. Data is collected
and analyzed to determine the level of student performance on these assessment instruments in
regards to meeting course objectives. The results of this data analysis are used to guide necessary
pedagogical and/or curricular revisions.
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Course Requirements: All students are required to:
1. Maintain regular attendance.
2. Complete assigned homework or projects in a timely manner.
3. Take part in class discussions and do problems on the board when required.
4. Take all tests and quizzes when scheduled. These include a minimum of three class tests as well as a
final exam.
5. Complete at least one group project and at least one individual project.
6. Conduct oral presentations. These include a minimum of one group and/or one individual
presentation on research projects.
Methods of Evaluation: Final course grades will be computed as follows:
% of
final course grade
Grading Components

Homework, quizzes, and class participation
0 – 15%
A perusal of homework problems and quizzes and class
discussion will indicate the extent to which students master
course objectives.

3 or more Tests (dates specified by the instructor)
30  60%
Tests will show evidence of the extent to which students meet
course objectives, including, but not limited to, identifying and
applying concepts, analyzing and solving problems, estimating
and interpreting results, and stating appropriate conclusions
using correct terminology.

20  25%
Group project(s)
The group project(s) demonstrate(s) students' ability to work
collaboratively on conducting research and presenting mathrelated topics. These projects will test preparation for
operating in the work place.

20  25%
Individual Project(s)
The individual project(s) demonstrate(s) student’s ability to
work individually on conducting research and presenting mathrelated topics.

10  15%
Final Exam
The comprehensive final exam will examine the extent to which
students have understood and synthesized all course content
and achieved all course objectives.
NOTE: The instructor will provide specific weights, which lie in the above-given ranges, for each of the
grading components at the beginning of the semester. Also, see page 7 for suggested topics for group
and/or individual research projects.
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Academic Integrity: Dishonesty disrupts the search for truth that is inherent in the learning process and
so devalues the purpose and the mission of the College. Academic dishonesty includes, but is not
limited to, the following:

plagiarism – the failure to acknowledge another writer’s words or ideas or to give proper credit
to sources of information;

cheating – knowingly obtaining or giving unauthorized information on any test/exam or any
other academic assignment;

interference – any interruption of the academic process that prevents others from the proper
engagement in learning or teaching; and

fraud – any act or instance of willful deceit or trickery.
Violations of academic integrity will be dealt with by imposing appropriate sanctions. Sanctions for acts
of academic dishonesty could include the resubmission of an assignment, failure of the test/exam,
failure in the course, probation, suspension from the College, and even expulsion from the College.
Student Code of Conduct: All students are expected to conduct themselves as responsible and
considerate adults who respect the rights of others. Disruptive behavior will not be tolerated. All
students are also expected to attend and be on time all class meetings. No cell phones or similar
electronic devices are permitted in class. Please refer to the Essex County College student handbook,
Lifeline, for more specific information about the College’s Code of Conduct and attendance
requirements.
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Course Content Outline: based on the text Mathematical Ideas, expanded 11th edition, by Miller,
Heeren & Hornsby; published by Addison-Wesley, 2008
Class Meeting
(80 minutes)
Chapter/Section
1
2
3
4
5
CHAPTER 1 INTRODUCTION AND OVERVIEW
1.1
Solving Problems by Inductive & Deductive Reasoning
1.2
An Application of Inductive Reasoning…Number Patterns
1.3
Strategies for Problem Solving
1.4
Calculating, Estimating and Reading Graphs
Read about Journal Writing & Discovering Patterns in Pascal’s Triangle
10
11
CHAPTER 2 BASIC CONCEPTS OF SET THEORY
2.1
Symbols and Terminology
2.2
Venn Diagrams and Subsets
2.3
Set Operations and Cartesian Products
2.3
Set Operations and Cartesian Products (continued)
2.4
Surveys and Cardinal Numbers
2.4
Surveys and Cardinal Numbers (continued)
2.5
Infinite Sets and Their Cardinalities
12
Test #1 on Chapters 1 & 2
6
7
8
9
13
14
15
16 – 17
18
CHAPTER 4 MATHEMATICAL SYSTEMS
4.1
Historical Mathematical Systems
4.2
Mathematics in the Hindu Arabic System
4.3
Conversion Between the Bases
4.4
Clock Arithmetic and the Modular Systems
Read and explore “A Perpetual Calendar”
4.5
Extension: Logic Problems and Sudoku
Logic Problems and Sudoku Revisited
19
20
21
22
23
CHAPTER 5 NUMBER THEORY
5.1
Prime and Composite Numbers
5.2
Selected Topics from Number Theory
5.3
Greatest Common Factor and Least Common Multiple
5.4
The Fibonacci Sequence and the Golden Ratio
Magic Squares
24
Test # 2 on Chapters 4 & 5
CHAPTER 8 GRAPHS
8.1
Rectangular Coordinate Systems and Circles
8.1
Rectangular Coordinate Systems and Circles (continued)
8.2
Lines, Slopes and Average Rate of Change
8.2
Lines, Slopes and Average Rate of Change (continued)
25
26
27
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Class Meeting
(80 minutes)
Chapter/Section
32
CHAPTER 9 GEOMETRY
9.2
Curves, Polygons and Circles
9.3
Perimeter, Area, and Circumference
9.4
The Geometry of Triangles: Congruence, Similarity and the Pythagorean
Theorem
9.4
The Geometry of Triangles: Congruence, Similarity and the Pythagorean
Theorem (continued)
9.5
Space Figures, Volumes and Surface Areas
9.5
Space Figures, Volumes and Surface Areas (continued)
33
34
35
36
CHAPTER 11 COUNTING METHODS
11.1 Counting by Systematic Listing
11.2 Using the Fundamental Counting Principle
11.3 Using Permutations and Combinations
11.4 Using Pascal’s Triangle and the Binomial Theorem
37
Test #3 on Chapters 8, 9 & 11
38 – 39
40
Group Presentations
Individual Presentations
41
42
Review for Final Exam
Comprehensive Final Exam on all course material covered
28
29
30
31
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MTH 103 – Suggested Topics for Individual and Group Research Projects
1.
The life and Work of “A Female Mathematician” or “A Mathematician from Your Culture”
2.
Pascal’s Triangle
3.
Using Modular Arithmetic to compute dates, times, etc.
4.
What Mathematics Means to Me
5.
Mathematics in Everyday Life
6.
Mathematics in the Workplace
7.
Problem Solving Techniques
8.
Euclidean Solids (Theory and Applications)
9.
Mathematics in the Family
10.
Multicultural Mathematics
11.
Creation and Presentation of Mathematical Puzzles
12.
The Golden Ratio
13.
The Origin of Zero
14.
Magic Squares
15.
The Fibonacci Sequence
16.
The Four Color Theorem
17.
Mathematics and Science
18.
Mathematics and Music
19.
Mathematics and Technology
20.
A Mathematical Topic of Your Choice
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MTH 103 – Suggested Homework Problems
TEXT: Mathematical Ideas, expanded 11th edition, by Miller, Heeren & Hornsby; published by AddisonWesley, 2008
Section
Homework page and numbers________________________________________
1.1
p. 7 # 1-13,15,17,20,22,27,31,33,41,43,45
1.2
p. 17 # 1-5,10,11,15,16,20,21-28,29,33,34,35,36,43,45,47
1.3
p. 27 # 1,2,5,8,10,20,24,33,39,50,57,63,69
1.4
p. 38 # 2,4,8,14,16,21,23,25,27,32,37,39,40,47,49,50,53,54,58,60,61,64
Journal Writing p. 42 Activities 1,2,5,6
Pascal’s Triangle p. 47 # 1-4
2.1
p. 56 # 2,4,6,8,9,13,16,18,21,24,25,28,29,31,33,35,38,40,41,43,45,46,47,53,56,58,59,60,
64,66,69,73, 76,80,83,88,91,94
2.2
p. 63 # 1,3,4,7,9,12,15,18,20,23,26,30,33,35,37,40,43,46,50,51,53,72
2.3
p. 75 # 1-8,12,13,15,16,18,20,21,23,24,29,30,31,32,36,49,50,52,53,54,55,58,59,63,65,
67,70,71-74,79,81,83,87,90,92,93,94,96,97,100,102,106,107,109,114,117,124,
128,129,132
2.4
p. 82 # 1,3,5,7,10,11,12,18,19,21,26,30
2.5
p. 92 # 1-6,7,8,11,12,16,18,21,24,25,28,29,31,33,34,37,39,41,43,45,47,49
4.1
p. 166 # 1,3,5,7,9,10,12,15,17,20,21,27,28,31,35,37,39,41,45,47,49
4.2
p. 177 # 1,3,6,9,11,14,15,17,20,21,23,26,27,29,31,33,35,38,39,41,43,45,47,50,51
4.3
p. 187 # 1-19 odd,24,29,31,36,42,43,45,47,49,51,53,55,59,61,63,66
4.4
p. 199 # 1-7 odd,8,9,10,13,14,15,16,17,18,19,22,25,27,29-35,39,42,46,47,48,49,53,56,
57,58,61
Calendar
p. 219 # 1
4.5
p. 141 # 1,2,5,6,7,9,11
5.1
p. 230 # 1,2,3,6,8,10,11,13,15,19,20,23,27,30,33,34,38,39,43,48,52,55,59,62,69,71,75,
80,81,84
5.2
p. 238 # 1,2,5,7,9,22,27-30,33,34,36,40,59
5.3
p. 247 # 1-47 odd,51,53
5.4
p. 262 # 1,3,7,9,13,15,18,20,25,27,31,34,35
Magic Squares p. 267 # 1,2,5,11,13,17,22,26,33,36
8.1
p. 438 # 1,3,4,5,6,7,9,11,12,13,14,18,19,21,24,25,28,29,31,33,35,39,41,43,45,47,50,52,
53,58,60,63,65,66,68,69
8.2
p. 447 # 1,2,3,6,7,9,10,11,13-39 odd, 40,41,43,46,47,49,51,53,55,56,57,59,60,65,67,69
9.2
p. 545 # 1-16,19,21,22,23,26,27-53 odd
9.3
p. 559 # 1-8,11,13,15,16,17,19,20,21,23,25,27,31,41-49,52,54,55,59,62,63,68
9.4
p. 572 # 1-39 odd, 41-73 odd, 77,78,81,83,84,86,88,89
9.5
p. 584 # 1,2,4,5,8-19,21,25,27,37,39,41,42,45-54
11.1
p. 678 # 1,10,13,16,17,20,23,24,26,28,29,32,34,36,37,39,40,43,44,45,47,51,54,55,57,59,
61,62,67
11.2
p. 689 # 1-7,9,11,13,16,17,22,26,27,29,31,33,35,37-42,47,49,50,55,57,60,61
11.3
p. 702 # 1-59 odd
11.4
p. 710 # 1-35 odd
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prepared by C Castillo & K Christie-Powell, Spring 2010